A pony tail palm is a succulent tree with a swollen bulb for a base and a thinner trunk with thin leaves sprouting from the top. It is not actually a palm tree, but grows outdoors in semi-desert areas and is a low-maintenance house plant. Propagation of a pony tail palm can be done by seeds, but the seeds are extremely rare and difficult to find. A better option is to wait until your tree develops offshoots on its swollen bulb and root those for a new plant.
Start propagation in the spring. Obtain a pot with good drainage and fill it with a well-drained potting soil. The roots do not need much water and actually thrive with some air, so it is essential that the potting medium be porous for drainage.
Cut an offshoot off of the pony tail palm with a knife and apply a bit of rooting hormone onto the end that was attached to the bulb. Follow the directions on the package while applying.
Plant the offshoot with the rooting hormone end pointed down about 1/3 of its length into the soil. Tamp the potting soil down around the shoot to keep it standing straight.
Place the planted offshoot in a window with full sun. Water it with only enough water to moisten it. Allow it to dry and then moisten it again. Keep this pattern until the offshoot begins to grow.